Multiply the following complex numbers: $({-5i}) \cdot ({1+2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5i}) \cdot ({1+2i}) = $ $ ({0} \cdot {1}) + ({0} \cdot {2}i) + ({-5}i \cdot {1}) + ({-5}i \cdot {2}i) $ Then simplify the terms: $ (0) + (0i) + (-5i) + (-10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 - 5)i - 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 - 5)i - (-10) $ The result is simplified: $ (0 + 10) + (-5i) = 10-5i $